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The Fourier-Jacobi Periods : The case of $Mp(2n+2r) \times Sp(2n)$

Published 10 Jan 2022 in math.NT and math.RT | (2201.03270v2)

Abstract: In this paper, we prove one direction of the Gan--Gross--Prasad conjecture on metaplectic-symplectic groups for tempered cases. Furthermore, we also prove one direction of the non-tempered GGP conjecture for residual representations with relevant $A$-parameters. As an application, we discuss the non-vanishing of the central value of quadratic twists of automorphic $L$-functions of $GL_{2n}$.

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